static void tst6() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
nlsat::var x0, x1, x2, a, b, c, d;
a = s.mk_var(false);
b = s.mk_var(false);
c = s.mk_var(false);
d = s.mk_var(false);
x0 = s.mk_var(false);
x1 = s.mk_var(false);
x2 = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
polynomial_ref _x0(pm), _x1(pm), _x2(pm);
polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
_x2 = pm.mk_polynomial(x2);
_a = pm.mk_polynomial(a);
_b = pm.mk_polynomial(b);
_c = pm.mk_polynomial(c);
_d = pm.mk_polynomial(d);
p1 = (_a*(_x0^2)) + _x2 + 2;
p2 = (_b*_x1) - (2*_x2) - _x0 + 8;
nlsat::scoped_literal_vector lits(s);
lits.push_back(mk_gt(s, p1));
lits.push_back(mk_gt(s, p2));
lits.push_back(mk_gt(s, (_c*_x0) + _x2 + 1));
lits.push_back(mk_gt(s, (_d*_x0) - _x1 + 5*_x2));
scoped_anum zero(am), one(am), two(am);
am.set(zero, 0);
am.set(one, 1);
am.set(two, 2);
as.set(0, one);
as.set(1, one);
as.set(2, two);
as.set(3, two);
as.set(4, two);
as.set(5, one);
as.set(6, one);
s.set_rvalues(as);
project(s, ex, x0, 2, lits.c_ptr());
project(s, ex, x1, 3, lits.c_ptr());
project(s, ex, x2, 3, lits.c_ptr());
project(s, ex, x2, 2, lits.c_ptr());
project(s, ex, x2, 4, lits.c_ptr());
project(s, ex, x2, 3, lits.c_ptr()+1);
}
static void tst7() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::var x0, x1, x2, a, b, c, d;
a = s.mk_var(false);
b = s.mk_var(false);
c = s.mk_var(false);
d = s.mk_var(false);
x0 = s.mk_var(false);
x1 = s.mk_var(false);
x2 = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
polynomial_ref _x0(pm), _x1(pm), _x2(pm);
polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
_x2 = pm.mk_polynomial(x2);
_a = pm.mk_polynomial(a);
_b = pm.mk_polynomial(b);
_c = pm.mk_polynomial(c);
_d = pm.mk_polynomial(d);
p1 = _x0 + _x1;
p2 = _x2 - _x0;
p3 = (-1*_x0) - _x1;
nlsat::scoped_literal_vector lits(s);
lits.push_back(mk_gt(s, p1));
lits.push_back(mk_gt(s, p2));
lits.push_back(mk_gt(s, p3));
nlsat::literal_vector litsv(lits.size(), lits.c_ptr());
lbool res = s.check(litsv);
SASSERT(res == l_false);
for (unsigned i = 0; i < litsv.size(); ++i) {
s.display(std::cout, litsv[i]);
std::cout << " ";
}
std::cout << "\n";
litsv.reset();
litsv.append(2, lits.c_ptr());
res = s.check(litsv);
SASSERT(res == l_true);
s.display(std::cout);
s.am().display(std::cout, s.value(x0));
std::cout << "\n";
s.am().display(std::cout, s.value(x1));
std::cout << "\n";
s.am().display(std::cout, s.value(x2));
std::cout << "\n";
}
void TestEval::apply01() {
const ExprSymbol& x1 = ExprSymbol::new_("x1");
const ExprSymbol& x2 = ExprSymbol::new_("x2");
Function f1(x1,x1,"f1");
Function f2(x2,f1(x2));
IntervalVector _x2(1,Interval(2,2));
check(f2.eval(_x2), Interval(2,2));
CPPUNIT_ASSERT((f2.eval(_x2)).is_superset(Interval(2,2)));
}
static void tst8() {
params_ref ps;
reslimit rlim;
nlsat::solver s(rlim, ps);
anum_manager & am = s.am();
nlsat::pmanager & pm = s.pm();
nlsat::assignment as(am);
nlsat::explain& ex = s.get_explain();
nlsat::var x0, x1, x2, a, b, c, d;
a = s.mk_var(false);
b = s.mk_var(false);
c = s.mk_var(false);
d = s.mk_var(false);
x0 = s.mk_var(false);
x1 = s.mk_var(false);
x2 = s.mk_var(false);
polynomial_ref p1(pm), p2(pm), p3(pm), p4(pm), p5(pm);
polynomial_ref _x0(pm), _x1(pm), _x2(pm);
polynomial_ref _a(pm), _b(pm), _c(pm), _d(pm);
_x0 = pm.mk_polynomial(x0);
_x1 = pm.mk_polynomial(x1);
_x2 = pm.mk_polynomial(x2);
_a = pm.mk_polynomial(a);
_b = pm.mk_polynomial(b);
_c = pm.mk_polynomial(c);
_d = pm.mk_polynomial(d);
scoped_anum zero(am), one(am), two(am), six(am);
am.set(zero, 0);
am.set(one, 1);
am.set(two, 2);
am.set(six, 6);
as.set(0, two); // a
as.set(1, one); // b
as.set(2, six); // c
as.set(3, zero); // d
as.set(4, zero); // x0
as.set(5, zero); // x1
as.set(6, two); // x2
s.set_rvalues(as);
nlsat::scoped_literal_vector lits(s);
lits.push_back(mk_eq(s, (_a*_x2*_x2) - (_b*_x2) - _c));
project(s, ex, x2, 1, lits.c_ptr());
}
static void *parallel64_t(void *input) {
int i;
threads64_t *in = (threads64_t *) input;
const int start = in->thread * in->size / NUM_THREADS;
const int stop = in->thread + 1 == NUM_THREADS ? in->size : (in->thread + 1) * in->size / NUM_THREADS;
const int curr = in->thread * HIST_SIZE;
uint32_t *A = &in->histA[curr];
uint32_t *B = &in->histB[curr];
uint32_t *C = &in->histC[curr];
uint32_t *D = &in->histD[curr];
uint32_t *E = &in->histE[curr];
uint32_t *F = &in->histF[curr];
for (i=start;i<stop;++i) {
const uint64_t pos = (in->array[i] = in->position(in->array[i]));
A[_x1(pos)]++;
B[_x2(pos)]++;
C[_x3(pos)]++;
D[_x4(pos)]++;
E[_x5(pos)]++;
F[_x6(pos)]++;
}
pthread_exit(NULL);
}
/* unconditional Monte Carlo simulation for discrete tests. */
SEXP mcarlo_mean(SEXP x, SEXP y, SEXP lx, SEXP ly, SEXP length, SEXP samples,
SEXP test) {
double *fact = NULL, *res = NULL, observed = 0;
int *n = NULL, *ncolt = NULL, *nrowt = NULL, *workspace = NULL;
int *num = INTEGER(length), *nr = INTEGER(lx), *nc = INTEGER(ly);
int *xx = INTEGER(x), *yy = INTEGER(y), *B = INTEGER(samples);
int i = 0, k = 0, npermuts = 0;
SEXP result;
/* allocate and initialize the result. */
PROTECT(result = allocVector(REALSXP, 3));
res = REAL(result);
res[0] = res[1] = res[2] = 0; // initial test score / mean score / nb permutations
/* allocate and compute the factorials needed by rcont2. */
allocfact(*num);
/* allocate and initialize the workspace for rcont2. */
workspace = alloc1dcont(*nc);
/* initialize the contingency table. */
n = alloc1dcont(*nr * (*nc));
/* initialize the marginal frequencies. */
nrowt = alloc1dcont(*nr);
ncolt = alloc1dcont(*nc);
/* compute the joint frequency of x and y. */
for (k = 0; k < *num; k++)
n[CMC(xx[k] - 1, yy[k] - 1, *nr)]++;
/* compute the marginals. */
for (i = 0; i < *nr; i++)
for (k = 0; k < *nc; k++) {
nrowt[i] += n[CMC(i, k, *nr)];
ncolt[k] += n[CMC(i, k, *nr)];
}/*FOR*/
/* initialize the random number generator. */
GetRNGstate();
/* pick up the observed value of the test statistic, then generate a set of
random contingency tables (given row and column totals) and adds their
test scores to compute the mean.*/
switch(INT(test)) {
case MUTUAL_INFORMATION:
observed = 2 * _mi(n, nrowt, ncolt, nr, nc, num);
for (k = 0; k < *B; k++) {
rcont2(nr, nc, nrowt, ncolt, num, fact, workspace, n);
res[1] += 2 * _mi(n, nrowt, ncolt, nr, nc, num);
npermuts++;
}
break;
case PEARSON_X2:
observed = _x2(n, nrowt, ncolt, nr, nc, num);
for (k = 0; k < *B; k++) {
rcont2(nr, nc, nrowt, ncolt, num, fact, workspace, n);
res[1] += _x2(n, nrowt, ncolt, nr, nc, num);
npermuts++;
}
break;
}/*SWITCH*/
PutRNGstate();
/* save the observed and mean values of the statistic,
and the number of permutations performed. */
res[0] = observed;
res[1] /= *B; // mean
res[2] = npermuts;
UNPROTECT(1);
return result;
}/*MCARLO_MEAN*/
/* unconditional Monte Carlo simulation for discrete tests. */
SEXP mcarlo(SEXP x, SEXP y, SEXP lx, SEXP ly, SEXP length, SEXP samples,
SEXP test, SEXP alpha) {
double *fact = NULL, *res = NULL, observed = 0;
int *n = NULL, *ncolt = NULL, *nrowt = NULL, *workspace = NULL;
int *num = INTEGER(length), *nr = INTEGER(lx), *nc = INTEGER(ly);
int *xx = INTEGER(x), *yy = INTEGER(y), *B = INTEGER(samples);
int i = 0, k = 0, npermuts = 0, enough = ceil(NUM(alpha) * (*B)) + 1;
SEXP result;
/* allocate and initialize the result. */
PROTECT(result = allocVector(REALSXP, 3));
res = REAL(result);
res[0] = res[1] = res[2] = 0; // initial test score / p-value / nb permutations
/* allocate and compute the factorials needed by rcont2. */
allocfact(*num);
/* allocate and initialize the workspace for rcont2. */
workspace = alloc1dcont(*nc);
/* initialize the contingency table. */
n = alloc1dcont(*nr * (*nc));
/* initialize the marginal frequencies. */
nrowt = alloc1dcont(*nr);
ncolt = alloc1dcont(*nc);
/* compute the joint frequency of x and y. */
for (k = 0; k < *num; k++)
n[CMC(xx[k] - 1, yy[k] - 1, *nr)]++;
/* compute the marginals. */
for (i = 0; i < *nr; i++)
for (k = 0; k < *nc; k++) {
nrowt[i] += n[CMC(i, k, *nr)];
ncolt[k] += n[CMC(i, k, *nr)];
}/*FOR*/
/* initialize the random number generator. */
GetRNGstate();
/* pick up the observed value of the test statistic, then generate a set of
random contingency tables (given row and column totals) and check how many
tests are greater than the original one.*/
switch(INT(test)) {
case MUTUAL_INFORMATION:
observed = _mi(n, nrowt, ncolt, nr, nc, num);
for (k = 0; k < *B; k++) {
rcont2(nr, nc, nrowt, ncolt, num, fact, workspace, n);
if (_mi(n, nrowt, ncolt, nr, nc, num) > observed) {
sequential_counter_check(res[1]);
}/*THEN*/
npermuts++;
}/*FOR*/
observed = 2 * observed;
break;
case PEARSON_X2:
observed = _x2(n, nrowt, ncolt, nr, nc, num);
for (k = 0; k < *B; k++) {
rcont2(nr, nc, nrowt, ncolt, num, fact, workspace, n);
if (_x2(n, nrowt, ncolt, nr, nc, num) > observed) {
sequential_counter_check(res[1]);
}/*THEN*/
npermuts++;
}/*FOR*/
break;
}/*SWITCH*/
PutRNGstate();
/* save the observed value of the statistic, the corresponding
p-value, and the number of permutations performed. */
res[0] = observed;
res[1] /= (*B);
res[2] = npermuts;
UNPROTECT(1);
return result;
}/*MCARLO*/